{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T12:39:40Z","timestamp":1778762380699,"version":"3.51.4"},"reference-count":40,"publisher":"American Mathematical Society (AMS)","issue":"340","license":[{"start":{"date-parts":[[2023,11,21]],"date-time":"2023-11-21T00:00:00Z","timestamp":1700524800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["CGSD3 - 534997 - 2019"],"award-info":[{"award-number":["CGSD3 - 534997 - 2019"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-05606-2015"],"award-info":[{"award-number":["RGPIN-05606-2015"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["CGSD3 - 534997 - 2019"],"award-info":[{"award-number":["CGSD3 - 534997 - 2019"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["RGPIN-05606-2015"],"award-info":[{"award-number":["RGPIN-05606-2015"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier\u2013Stokes equations. Key features of the numerical scheme include pointwise mass conservation, energy stability, and pressure robustness. We prove that there exists a solution to the resulting nonlinear algebraic system in two and three spatial dimensions, and that this solution is unique in two spatial dimensions under a small data assumption. A priori error estimates are derived for the velocity in a mesh-dependent energy norm.<\/p>","DOI":"10.1090\/mcom\/3796","type":"journal-article","created":{"date-parts":[[2022,10,6]],"date-time":"2022-10-06T08:21:14Z","timestamp":1665044474000},"page":"525-556","source":"Crossref","is-referenced-by-count":14,"title":["Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier\u2013Stokes equations"],"prefix":"10.1090","volume":"92","author":[{"given":"Keegan","family":"Kirk","sequence":"first","affiliation":[]},{"given":"Tam\u00e1s","family":"Horv\u00e1th","sequence":"additional","affiliation":[]},{"given":"Sander","family":"Rhebergen","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2022,11,21]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"3113","DOI":"10.1093\/imanum\/draa053","article-title":"Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier-Stokes equations","volume":"41","author":"Ahmed, Naveed","year":"2021","journal-title":"IMA J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-4979","issn-type":"print"},{"key":"2","doi-asserted-by":"crossref","unstructured":"R. Anderson, J. Andrej, A. Barker, J. Bramwell, J.-S. Camier, J. Cerveny V. Dobrev, Y. Dudouit, A. Fisher, Tz. Kolev, W. Pazner, M. Stowell, V. Tomov, I. Akkerman, J. Dahm, D. Medina, and S. Zampini, MFEM: a modular finite element methods library, Comput. Math. App. 81 (2021), 42\u201374.","DOI":"10.1016\/j.camwa.2020.06.009"},{"issue":"4","key":"3","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/BF02576171","article-title":"A stable finite element for the Stokes equations","volume":"21","author":"Arnold, D. N.","year":"1984","journal-title":"Calcolo","ISSN":"https:\/\/id.crossref.org\/issn\/0008-0624","issn-type":"print"},{"key":"4","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36519-5","volume-title":"Mixed finite element methods and applications","volume":"44","author":"Boffi, Daniele","year":"2013","ISBN":"https:\/\/id.crossref.org\/isbn\/9783642365188"},{"issue":"318","key":"5","doi-asserted-by":"publisher","first-page":"1559","DOI":"10.1090\/mcom\/3405","article-title":"Spectral approximation of elliptic operators by the hybrid high-order method","volume":"88","author":"Calo, Victor","year":"2019","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"306","key":"6","doi-asserted-by":"publisher","first-page":"1643","DOI":"10.1090\/mcom\/3195","article-title":"Analysis of a hybridizable discontinuous Galerkin method for the steady-state incompressible Navier-Stokes equations","volume":"86","author":"Cesmelioglu, Aycil","year":"2017","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"7","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1137\/030602289","article-title":"Error estimates for the discontinuous Galerkin methods for parabolic equations","volume":"44","author":"Chrysafinos, K.","year":"2006","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"1","key":"8","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1051\/m2an:2007053","article-title":"Lagrangian and moving mesh methods for the convection diffusion equation","volume":"42","author":"Chrysafinos, Konstantinos","year":"2008","journal-title":"M2AN Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"issue":"272","key":"9","doi-asserted-by":"publisher","first-page":"2135","DOI":"10.1090\/S0025-5718-10-02348-3","article-title":"Discontinuous Galerkin approximations of the Stokes and Navier-Stokes equations","volume":"79","author":"Chrysafinos, Konstantinos","year":"2010","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"10","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1137\/070706616","article-title":"Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems","volume":"47","author":"Cockburn, Bernardo","year":"2009","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"246","key":"11","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1090\/S0025-5718-03-01552-7","article-title":"The local discontinuous Galerkin method for the Oseen equations","volume":"73","author":"Cockburn, Bernardo","year":"2004","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"12","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1137\/S0036142900380121","article-title":"Local discontinuous Galerkin methods for the Stokes system","volume":"40","author":"Cockburn, Bernardo","year":"2002","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"13","first-page":"33","article-title":"Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I","volume":"7","author":"Crouzeix, M.","year":"1973","journal-title":"Rev. Fran\\c{c}aise Automat. Informat. Recherche Op\\'{e}rationnelle S\\'{e}r. Rouge"},{"key":"14","series-title":"Math\\'{e}matiques \\& Applications (Berlin) [Mathematics \\& Applications]","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-22980-0","volume-title":"Mathematical aspects of discontinuous Galerkin methods","volume":"69","author":"Di Pietro, Daniele Antonio","year":"2012","ISBN":"https:\/\/id.crossref.org\/isbn\/9783642229794"},{"key":"15","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-19267-3","volume-title":"Discontinuous Galerkin method","volume":"48","author":"Dolej\u0161\u00ed, V\u00edt","year":"2015","ISBN":"https:\/\/id.crossref.org\/isbn\/9783319192666"},{"key":"16","series-title":"SpringerBriefs in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-27230-2","volume-title":"An invitation to the theory of the hybridizable discontinuous Galerkin method","author":"Du, Shukai","year":"2019","ISBN":"https:\/\/id.crossref.org\/isbn\/9783030272296"},{"issue":"268","key":"17","doi-asserted-by":"publisher","first-page":"1919","DOI":"10.1090\/S0025-5718-09-02243-1","article-title":"A symmetric error estimate for Galerkin approximations of time-dependent Navier-Stokes equations in two dimensions","volume":"78","author":"Dupont, Todd F.","year":"2009","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"18","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/s10492-007-0011-8","article-title":"Space-time discontinuous Galerkin method for solving nonstationary convection-diffusion-reaction problems","volume":"52","author":"Feistauer, Miloslav","year":"2007","journal-title":"Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0862-7940","issn-type":"print"},{"issue":"2","key":"19","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/s00211-010-0348-x","article-title":"Analysis of space-time discontinuous Galerkin method for nonlinear convection-diffusion problems","volume":"117","author":"Feistauer, Miloslav","year":"2011","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"20","series-title":"Springer Monographs in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09620-9","volume-title":"An introduction to the mathematical theory of the Navier-Stokes equations","author":"Galdi, G. P.","year":"2011","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387096193","edition":"2"},{"key":"21","unstructured":"P. Hood and C. Taylor, Navier\u2013Stokes equations using mixed interpolation, Finite Element Methods in Flow Problems, University of Alabama in Huntsville Press, 1974, pp. 121\u2013132."},{"issue":"12","key":"22","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1002\/fld.4707","article-title":"A locally conservative and energy-stable finite-element method for the Navier-Stokes problem on time-dependent domains","volume":"89","author":"Horv\u00e1th, Tam\u00e1s L.","year":"2019","journal-title":"Internat. J. Numer. Methods Fluids","ISSN":"https:\/\/id.crossref.org\/issn\/0271-2091","issn-type":"print"},{"key":"23","doi-asserted-by":"publisher","first-page":"109577","DOI":"10.1016\/j.jcp.2020.109577","article-title":"An exactly mass conserving space-time embedded-hybridized discontinuous Galerkin method for the Navier-Stokes equations on moving domains","volume":"417","author":"Horv\u00e1th, Tam\u00e1s L.","year":"2020","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"issue":"4","key":"24","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1007\/s00211-011-0372-5","article-title":"Inf-sup conditions for twofold saddle point problems","volume":"118","author":"Howell, Jason S.","year":"2011","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"key":"25","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-45750-5","volume-title":"Finite element methods for incompressible flow problems","volume":"51","author":"John, Volker","year":"2016","ISBN":"https:\/\/id.crossref.org\/isbn\/9783319457499"},{"issue":"3","key":"26","doi-asserted-by":"publisher","first-page":"492","DOI":"10.1137\/15M1047696","article-title":"On the divergence constraint in mixed finite element methods for incompressible flows","volume":"59","author":"John, Volker","year":"2017","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/1095-7200","issn-type":"print"},{"issue":"4","key":"27","doi-asserted-by":"publisher","first-page":"1677","DOI":"10.1137\/18M1202049","article-title":"Analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem on time-dependent domains","volume":"57","author":"Kirk, K. L. A.","year":"2019","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"28","unstructured":"MFEM: modular finite element methods [software], \\url{mfem.org}."},{"issue":"11","key":"29","doi-asserted-by":"publisher","first-page":"4185","DOI":"10.1016\/j.jcp.2012.02.011","article-title":"A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains","volume":"231","author":"Rhebergen, Sander","year":"2012","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"key":"30","isbn-type":"print","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/978-0-8176-8394-8_4","article-title":"Space-time hybridizable discontinuous Galerkin method for the advection-diffusion equation on moving and deforming meshes","author":"Rhebergen, Sander","year":"2013","ISBN":"https:\/\/id.crossref.org\/isbn\/9780817683931"},{"key":"31","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/j.jcp.2012.08.052","article-title":"A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations","volume":"233","author":"Rhebergen, Sander","year":"2013","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"},{"issue":"3","key":"32","doi-asserted-by":"publisher","first-page":"1936","DOI":"10.1007\/s10915-018-0760-4","article-title":"Preconditioning of a hybridized discontinuous Galerkin finite element method for the Stokes equations","volume":"77","author":"Rhebergen, Sander","year":"2018","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"key":"33","doi-asserted-by":"publisher","first-page":"112619","DOI":"10.1016\/j.cma.2019.112619","article-title":"An embedded-hybridized discontinuous Galerkin finite element method for the Stokes equations","volume":"358","author":"Rhebergen, Sander","year":"2020","journal-title":"Comput. Methods Appl. Mech. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0045-7825","issn-type":"print"},{"issue":"4","key":"34","doi-asserted-by":"publisher","first-page":"1982","DOI":"10.1137\/16M1083839","article-title":"Analysis of a hybridized\/interface stabilized finite element method for the Stokes equations","volume":"55","author":"Rhebergen, Sander","year":"2017","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"3","key":"35","doi-asserted-by":"publisher","first-page":"1484","DOI":"10.1007\/s10915-018-0671-4","article-title":"A hybridizable discontinuous Galerkin method for the Navier-Stokes equations with pointwise divergence-free velocity field","volume":"76","author":"Rhebergen, Sander","year":"2018","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"issue":"3","key":"36","doi-asserted-by":"publisher","first-page":"Paper No. 61, 38","DOI":"10.1007\/s10915-020-01340-8","article-title":"A space-time hybridizable discontinuous Galerkin method for linear free-surface waves","volume":"85","author":"Sosa Jones, Giselle","year":"2020","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"key":"37","series-title":"Studies in Mathematics and its Applications","isbn-type":"print","volume-title":"Navier-Stokes equations","volume":"2","author":"Temam, Roger","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/0444853073"},{"key":"38","series-title":"Springer Series in Computational Mathematics","isbn-type":"print","volume-title":"Galerkin finite element methods for parabolic problems","volume":"25","author":"Thom\u00e9e, Vidar","year":"2006","ISBN":"https:\/\/id.crossref.org\/isbn\/9783540331216","edition":"2"},{"issue":"12","key":"39","doi-asserted-by":"publisher","first-page":"1892","DOI":"10.1016\/j.apnum.2007.11.010","article-title":"A space-time discontinuous Galerkin method for the time-dependent Oseen equations","volume":"58","author":"van der Vegt, J. J. W.","year":"2008","journal-title":"Appl. Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0168-9274","issn-type":"print"},{"issue":"2","key":"40","first-page":"546","article-title":"Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. I. General formulation","volume":"182","author":"van der Vegt, J. J. W.","year":"2002","journal-title":"J. Comput. Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0021-9991","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-340\/S0025-5718-2022-03796-0\/mcom3796_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-340\/S0025-5718-2022-03796-0\/S0025-5718-2022-03796-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T04:48:33Z","timestamp":1776833313000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2023-92-340\/S0025-5718-2022-03796-0\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,21]]},"references-count":40,"journal-issue":{"issue":"340","published-print":{"date-parts":[[2023,3]]}},"alternative-id":["S0025-5718-2022-03796-0"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3796","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2022,11,21]]}}}